CAPM

In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM “suggests that an investor’s cost of equity capital is determined by beta.”[1]:2

The CAPM was introduced by Jack Treynor (1961, 1962),[2] William F. Sharpe (1964), John Lintner (1965a,b) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the 1990 Nobel Memorial Prize in Economics for this contribution to the field of financial economics. Fischer Black (1972) developed another version of CAPM, called Black CAPM or zero-beta CAPM, that does not assume the existence of a riskless asset. This version was more robust against empirical testing and was influential in the widespread adoption of the CAPM.

Despite its empirical flaws[3] and the existence of more modern approaches to asset pricing and portfolio selection (such as arbitrage pricing theory and Merton's portfolio problem), the CAPM still remains popular due to its simplicity and utility in a variety of situations.

Contents [hide]

1 Formula

2 Modified formula

3 Security market line

4 Asset pricing

5 Asset-specific required return

6 Risk and diversification

7 Efficient frontier

8 Market portfolio

9 Assumptions of CAPM

10 Problems of CAPM

11 See also

12 References

13 Bibliography

Formula[edit]

The security market line, seen here in a graph, describes a relation between the beta and the asset's expected rate of return.

The CAPM is a model for pricing an individual security or portfolio. For individual securities, we make use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:

\frac {E(R_i)- R_f}{\beta_{i}} = E(R_m) - R_f

The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for E(R_i)~~, we obtain the capital asset pricing model (CAPM).

E(R_i) = R_f + \beta_{i}(E(R_m) - R_f)\,

where:

E(R_i)~~ is the expected return on the capital asset

R_f~ is the risk-free rate of interest such as interest arising from government bonds

\beta_{i}~~ (the beta) is the sensitivity of the expected excess asset returns to the expected excess market returns, or also \beta_{i} = \frac {\mathrm{Cov}(R_i,R_m)}{\mathrm{Var}(R_m)},

E(R_m)~ is the expected return of the market

E(R_m)-R_f~ is sometimes known as the market premium (the difference between the expected market rate of return and the risk-free rate of return).

E(R_i)-R_f~ is also known as the risk premium

Restated, in terms of risk premium, we find that:

E(R_i) - R_f = \beta_{i}(E(R_m) - R_f)\,

which states that the individual risk premium equals the market premium times β.

Note 1: the expected market rate of return is usually estimated by measuring the arithmetic average of the historical returns on a market portfolio (e.g. S&P 500).

Note 2: the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk

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